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The case for splitting up the beverage and snacks business isn’t as clear-cut as Billionaire Nelson Peltz has argued. But keeping the company together isn’t working as well as the company says either.

Peltz is right that PEP stock has underperformed its peers significantly. Shares of Dr Pepper Snapple (DPS) have more than doubled since they began trading in May 2008 after it was spun-off from Cadbury at Peltz’s urging. Coca-Cola (KO), by far the world’s largest carbonated beverage company, posted a 56 percent gain in that time while PEP stock increased by just 31 percent.

Given that per-capita soda consumption is at a multi-decade low, it’s hard to believe that “freed of allocated corporate costs and bureaucracy, and able to be nimble and lean…a standalone beverage business will not only compete, but thrive.”

Peltz’s claim that DPS “has maneuvered both Coke and Pepsi over the past five years” is an exaggeration. According to Beverage Digest, when measured by volume, DPS’ market share as of the latest data available was 16.8 percent — nearly unchanged from the 16.4 percent seen in 2009. KO and PEP stock are still in the No. 1 and No. 2 positions, and neither has changed much during that time.

Much to the chagrin of Peltz, PepsiCo recently conducted a strategic review of its options and decided to keep things the same. Speaking during the recent earnings conference call, CEO Indra Nooyi argued the following:

“Decoupling our beverage and snack business in North America would significantly reduce our relevance to our customers. … In addition, we would forfeit a number of synergies within North America, including shared procurement, consumer and customer insights organizations, joint advertising, and use of major properties like the NFL and Major League Baseball, and joint promotional and display activity and coordinated national account activity.”

However, even if the snacks businesses were separated, it’s hard to imagine it doing much better than it is now. Revenue at PepsiCo’s Americas Foods business rose 5% to $25.08 billion in 2013 as strength in Frito-Lay off-set weakness in Quaker Foods.

Mondelez (MDLZ), the struggling maker of Cadbury chocolate and Oreo cookies, is forecasting sales growth this year of about 5% — well above the 1.3% gain analysts are expecting from PEP stock. MDLZ has failed to meet Wall Street expectations for the past two quarters.

Though Nooyi has repeatedly argued that the synergies between snacks and beverages are too compelling to ignore, the biggest innovation Frito-Lay has seen in years, the Doritos Locos Taco, didn’t come from the company. It was invented by marketing executive Todd Mills, who created a grass-roots campaign for the product and had no connection to PepsiCo.

Speaking of the “snacks” business, Peltz hasn’t specified what he means when he uses the term, and it’s easy to see why. PEP stock has two food businesses: Frito-Lay, a maker of potato and tortilla chips, and Quaker Foods, best known for its oatmeal. PepsiCo. acquired Frito-Lay in the 1960s and bought Quaker Foods in 2001. And you don’t have to be a billionaire to see which one is the better business.

Americans spend roughly $20 billion annually on salty snacks, according to data from Symphony/IRI. Oatmeal sales, according to data I found from 2010, are a paltry $427 million annually. Sales of ready-to-eat cereals such as Quaker’s Cap’n Crunch have been moribund for years. Other Quaker products such as Aunt Jemima pancake products and Rice-A-Roni can hardly be called snacks.

Though Coca-Cola is still dominating the soda war, PEP stock is the better stock for investors to buy. Since most of its growth is coming from snacks, it is less dependent on the carbonated beverage market, which is going to decline for years to come.

PEP stock trades at about a 12 percent discount to its average 52-week price target of $89.56. Moreover, its price-to-earnings multiple is about 18.2, less than Coca-Cola’s 19.7. Though KO has a slightly better upside and offers a dividend yield of 3.3% — better than PepsiCo’s 2.9% — Coca-Cola is in for a tough slog.

Regardless of whether Peltz’s efforts are successful, PEP stock will be in much better shape than its competition.

As of this writing, Jonathan Berr did not hold a position in any of the aforementioned securities.